Practically, system dynamics are nonlinear, requiring the estimation of unknown states, which encourages the observer schemes to be implanted in control structures. This dissertation presents estimation andltering of the Lipschitz and one-sided Lipschitz nonlinear systems and provides robustness against L2 normbounded disturbances and parameter uncertainties for state estimation. The developed approaches overcome the practical consequences of time-delays, perturbations and disturbances. Robust state estimation for Lipschitz and one-sided Lipschitz nonlinear systems is established by the adoption of Luenberger-like observer scheme, which is extended to the generalizedltering scheme to exhibit diverging manifolds, namely, the conventional static-gainlter and dynamiclter as speci c scenarios. Further, the presented estimation schemes unfolded the application based designs, including observer-based control of the nonlinear systems. Observer-based controller application is a duple process: It requires the estimation of unknown states atrst step, while in second stage, a controller is designed using these estimated states. A decoupling condition, necessary and su cient, for the presented approach, is explored to obtain controller and observer gains. Moreover, the controller scheme is further extended to overcome time-varying parametric uncertainties and norm-bounded disturbances. Convex optimization is adopted to solve the nonlinear constraints by combining nested bilinear-term-solver approach with a nonlinear optimization-based cone complimentary linearization. Comprehending the contributions of this dissertation, robust estimation based approaches for Lipschitz and one-sided Lipschitz systems are explored under output delays. Delay-range-dependent stability criterion is adopted to establish the stability, which foregrounds less conservative schemes. Robust generalizedltering for delayed nonlinear systems extends the concept of estimation tolter the noises and perturbations. Furthermore, robust estimation scheme for the nonlinear systems against parametric uncertainties is provided under measurement delay. Robust observer-based controller schemes as applications of the proposed estimation methods are studied. Numerical simulation results of practical systems are provided.